Nonlinear Coupling Coefficient Research Articles

Energy transfer in resonant and near-resonant internal wave triads for weakly non-uniform stratifications. Part 1. Unbounded domain

Abstract

Genuine quadripartite quantum steering generated by an optical parametric oscillation cascaded with a sum-frequency process

Quantum steering is the essential resource for quantum information processing. In this letter, a scheme is proposed to generate genuine quadripartite Einstein-Podolsky-Rosen (EPR) steering by an optical parametric oscillation cascaded with a sum-frequency process. Idler beam is generated by a difference frequency generation process between pump and injected signal in an optical superlattice. Then, a sum-frequency beam is produced by the cascaded sum-frequency process between pump and idler beams in the same optical superlattice by the quasi-phase-matching technique. The genuine quadripartite EPR steering among pump, signal, idler, and sum-frequency beams is confirmed in this scheme by applying a criteria for genuine multipartite EPR steering. The variation properties of the EPR steering with pump and nonlinear coupling coefficients are also discussed.

Nonlinear damping and mass effects of electromagnetic shunt damping for enhanced nonlinear vibration isolation

This paper investigates the nonlinear mass and damping effects of nonlinear electromagnetic shunt damping (N-EMSD) for vibration isolation performance enhancement of a permanent magnets (PMs) based nonlinear vibration isolator (NVI). An electromagnetic structure composing of two coils and two PMs is designed to realize equivalent nonlinear damping and mass. The nonlinear mechanic-electromagnetic coupling coefficient is analyzed and modeled. The voltage frequency of the circuit is twice the displacement frequency that is totally different with that of the linear electromagnetic shunt damping (L-EMSD). The amplitude frequency response function of the NVI with N-EMSD is theoretically derived via the harmonic balance method (HBM) and the stability is judged with Jacobian matrix. Then the equivalent nonlinear damping and nonlinear mass of the N-EMSD is derived. The numerical predictions agree with the experimental results, which demonstrate that the use of inductance in shunt circuit can change the equivalent nonlinear mass and the “jump” frequency of the NVI. Large value of inductance deteriorates the vibration isolation performance and the optimal inductance is slightly smaller than zero. Furthermore, N-EMSD can realize nonlinear damping to achieve wide band vibration isolation of the NVI. The optimal negative resistance is discussed.

Dynamics of a non-smooth type hybrid energy harvester with nonlinear magnetic coupling

In this paper, a system with energy harvester behavior is modeled by non-smooth coupled oscillators subjected to harmonic and random excitations. A modified harmonic balance method is proposed to study the dynamics of the oscillators under harmonic driving. Then, the probabilistic response of the system under bounded and colored noise excitations is tackled through the stochastic averaging method. We show that the proposed modified harmonic balance technique is very effective in parameters regime for which the system output waveform is nearly sinusoidal. In this parameters regime, the harvester performance is improved for optimum nonlinear magnetic coupling coefficients and for weak nonlinearities and damping in the harvester mechanical part. Under random excitations, we find in the weak parameters regime that, the probability density functions (PDFs) for the coupled oscillators amplitudes illustrate a single-peak mode and exhibit phenomenological transitions as the noisy excitations parameters vary. The mean output powers (MOPs) linearly increase with the colored noises intensities, and the piezoelectric MOP especially shows a resonance effect as the bounded noise level increases. Contrariwise, probed with Monte Carlo simulation, we find that the system exhibits the stochastic P-bifurcation for large parameters of coupling and nonlinearity; parameters’ regime for which the harvester under purely harmonic driving demonstrates low performance.

On the design of nonlinear damping with electromagnetic shunt damping

Traditional linear electromagnetic shunt damping (L-EMSD) has been studied deeply, however, the vibration isolation performance becomes worse with the increase of linear damping in the isolation region. To overcome the limitation of L-EMSD, this paper proposes two types of nonlinear electromagnetic shunt damping (N-EMSD) to develop nonlinear damping for the broadband vibration isolation of linear vibration isolators (LVIs). Both the two types of N-EMSD consist of two permanent magnets (PMs) and coils, however, the ways to connect to the external shunt circuits and the configurations between the PMs and coils are different. Nonlinear electromagnetic coupling coefficients are analyzed theoretically. The theoretical transmissibility of the LVI with N-EMSD is derived via the harmonic balance method (HBM). Numerical simulations and experiments are conducted to verify nonlinear damping performance of N-EMSD. The results demonstrate that compared to L-EMSD the proposed N-EMSD have similar vibration suppression performance in the resonance region, but are more effective in the isolation region.

Theoretical modeling and experimental analysis of nonlinear electromagnetic shunt damping

Linear electromagnetic shunt damping (L-EMSD) has been investigated deeply for vibration control in previous studies. This paper proposes nonlinear electromagnetic shunt damping (N-EMSD) for vibration isolation enhancement of linear vibration isolators (LVIs), which has not been discussed in existing literature. N-EMSD composes of a pair of the permanent magnets (PMs) and a pair of the coils, where the two coils are wound in opposite direction and connected in series. The nonlinear electromagnetic coupling coefficient is derived. The coupling governing equations of a LVI with N-EMSD are established and the amplitude-frequency relationship is theoretically derived using the harmonic balance method (HBM). Both the simulations and experiments are carried out to verify the nonlinear damping characteristic of N-EMSD. The results demonstrate that the LVI with N-EMSD can effectively reduce the vibration in the resonance region without affecting the vibration isolation performance in the isolation region compared with the traditional L-EMSD. It is also found in both simulation and experiment for the two coils configuration that the frequency of the induced voltage is twice the frequency of the displacement. Furthermore, the transmissibility of the LVI with N-EMSD reduces with the increase of the input amplitude in the resonance region, which demonstrates the nonlinearity of N-EMSD. The natural frequency slightly decreases with the decrease of the peak transmissibility. This paper extends the electromagnetic shunt damping (EMSD) technique from linear to nonlinear fields and provides a guideline to design nonlinear damping.

A bistable vibration isolator with nonlinear electromagnetic shunt damping

Abstract This paper presents a bistable vibration isolator (BVI) with several ring permanent magnets (PMs) and utilizes nonlinear electromagnetic shunt damping (N-EMSD) to improve the vibration isolation performance of the BVI. The theoretical model of N-EMSD is established. The harmonic balance method (HBM) is employed to derive the transmissibility of the BVI with N-EMSD. The analytical, numerical and experimental efforts are performed to investigate the vibration isolation performance of the BVI with N-EMSD. The results demonstrate that when the BVI is in the interwell oscillation, two peaks appear in the transmissibility curve and the transmissibility could be smaller than 1 between the two peaks. With the increase of the negative resistance, the motion of the BVI changes from the aperiodic/chaotic interwell oscillation to intrawell oscillation, resulting in the increase of the isolation band and the improved vibration isolation performance. The effects of the nonlinear electromagnetic coupling coefficient and the negative resistance are also investigated. The BVI with N-EMSD provides a feasible approach to study the vibration isolation characteristic of bistable structures.

Two- and three-mode intensity-difference squeezing in cascaded four-wave mixing inside an optical cavity

We report a theoretical study about the two- and three-mode intensity-difference squeezing inside an atom-like optical cavity. A cascaded parametric amplification four-wave mixing process is considered, and the cavity dressing and ‘dressing-like’ effects with different nonlinear coefficients affecting the degree of squeezing of the fluctuation spectra are researched. The altering of the nonlinear coupling coefficient changes the relationship between the cavity dressing and ‘dressing-like’ effects, which determines the squeezing degree and results in a new type of multi-dip squeezing and double-peak anti-squeezing.

Nonlinear Second-Order Topological Insulators.

We demonstrate, both theoretically and experimentally, the concept of nonlinear second-order topological insulators, a class of bulk insulators with quantized Wannier centers and a bulk polarization directly controlled by the level of nonlinearity. We show that one-dimensional edge states and zero-dimensional corner states can be induced in a trivial crystal insulator made of evanescently coupled resonators with linear and nonlinear coupling coefficients, simply by tuning the intensity. This allows global external control over topological phase transitions and switching to a phase with nonzero bulk polarization, without requiring any structural or geometrical changes. We further show how these nonlinear effects enable dynamic tuning of the spectral properties and localization of the topological edge and corner states. Such self-induced second-order topological insulators, which can be found and implemented in a wide variety of physical platforms ranging from electronics to microwaves, acoustics, and optics, hold exciting promises for reconfigurable topological energy confinement, power harvesting, data storage, and spatial management of high-intensity fields.

Nonlinear Electromagnetic Shunt Damping for Nonlinear Vibration Isolators

This paper presents the concept of nonlinear electromagnetic shunt damping (N-EMSD) and employs it for the vibration isolation enhancement of nonlinear vibration isolators. A nonlinear electromagnetic vibration isolator (NEVI) is designed. Two configurations of the permanent magnets and coils are constructed to illustrate the damping mechanisms of linear electromagnetic shunt damping (L-EMSD) and N-EMSD, respectively. The nonlinear electromagnetic coupling coefficient of the NEVI is modeled. The theoretical models of the NEVI with L-EMSD and N-EMSD are established. Both the numerical simulation and experimental efforts are performed to verify the vibration isolation performance of the NEVI with L-EMSD and N-EMSD. The results demonstrate that the proposed N-EMSD can provide wonderful nonlinear damping to reduce vibration in the resonance region but do not affect the isolation performance in the isolation region. L-EMSD has a better vibration suppression performance than N-EMSD in the resonance region; however, the vibration isolation performance becomes worse in the isolation region. Furthermore, the effect of the isolation mass is also studied experimentally. This work opens a new opportunity to further study EMSD technique in linear and nonlinear systems.

Uncertainty Analysis of Bistable Vibration Energy Harvesters Based on the Improved Interval Extension

PurposeHigh-energy interwell oscillations of the bistable energy harvester (BEH) lead to large-amplitude output voltage. For processing and manufacturing of the BEH, small errors and deviations in the final structure cannot be totally eliminated in practice, which will make the output voltage to be apart away from the design value. Therefore, the geometrical variables, material properties and other parameters should be treated as uncertainties in analysis and are bound to their design.MethodThis paper presents uncertainty analysis of the BEH to reveal the influence of the uncertain system parameters on the energy harvesting performance. The improved interval extension based on the first-order Taylor series is used to predict the lower and upper bounds of the stable high-energy interwell output voltage of the BEH. In detail, uncertain mass, nonlinear stiffness term, damping, capacitance and electromechanical coupling coefficient are considered. Meanwhile, the Monte Carlo simulation is employed to verify the suitability and the accuracy of this method. Especially, this method allows researchers to define the number of the parameter αj according to the categories of uncertain variables.ResultsThe research works show that interval of the output voltage of the BEH can be limited by reducing the number of uncertain variables, and the uncertainty of the output voltage is more sensitive to the electrical uncertain variables than the structural uncertainties.ConclusionDesigners of the BEH should pay enough attention to the errors and tolerances of the electrical output design variables. Specifically, in the design of the BEH, it is more effective to improve the accuracy of the output voltage by limiting the uncertainties of electric parameters than structural parameters. Reducing the number of uncertain parameters through increasing processing precision in production of the BEH can also improve the accuracy of the output voltage.

Polarization transformation of three light beams in sum-frequency generation in isotropic chiral medium in case of high conversion efficiency

Sum-frequency generation in the case of coaxial interaction of elliptically polarized Gaussian beams of fundamental radiation in isotropic chiral medium was studied. The system of three equations of nonlinear diffraction was solved numerically without the assumption of undepleting fundamental (‘pump’) waves. It has been shown that only for small (less than 0.1) values of nonlinear coupling coefficient of the interacting waves can their propagation be described within the framework of such approximation with precision of a few tenths of a percent. However, the results of the undepleting pump approximation are remarkably different from those obtained in the numerical solution of a system of nonlinear equations for greater values of nonlinear coupling coefficient. In the first turn, this difference appears in the amplitude and polarization of the sum frequency beam. When the nonlinear coupling coefficient is of the order of unity, its further increase does not lead to the growth of the conversion efficiency, which remains of the order of 10−2. At the same time, there appear to be notable changes of intensity and polarization of light in the transverse sections of the beams at fundamental frequencies.

Analytical solution of second-harmonic generation in a lithium-niobate-birefringence thin-film waveguide via modal phase matching

We present a systematic theoretical investigation of second-harmonic generation (SHG) in a subwavelength lithium niobate (LN) single-crystal thin-film waveguide with birefringence in permittivity and refractive index and strong anisotropy in the nonlinear susceptibility ${\ensuremath{\chi}}^{(2)}$. In a macroscopic birefringence LN crystal, the birefringence phase matching scheme that makes use of the refractive index management between the extraordinary light (EL) and ordinary light (OL) is dominantly used to ensure high-efficiency SHG. Yet, this scenario needs significant modification in a subwavelength LN thin film, where one should instead consider the waveguide modes of fundamental wave (FW) and second-harmonic wave (SHW) to participate in the SHG process. To this end, we first analytically solve and calculate the dispersion and modal profile of optical waveguide modes supported in the birefringence LN planar waveguide in a broad bandwidth ranging from ultraviolet to infrared regimes for TM (EL-like) and TE (OL-like) polarization states and at different waveguide thicknesses. Then we systematically examine the phase matching conditions that are necessary for high-efficiency energy conversion from FW waveguide mode to SHW waveguide mode via SHG. We find several modal phase matching schemes by exploiting the versatile freedoms of the FW and SHW waveguide mode number and polarization, and the waveguide thickness and symmetry. Yet modal phase matching only takes place at very limited discrete wavelengths of FW pump light. Under the modal phase matching condition, we derive the nonlinear coupled mode theory from Maxwell's equations and calculate the conversion efficiency of SHG, and find that the efficiency of SHG is determined by the nonlinear coupling coefficients that are closely associated with the modal profile overlap extent and mode transition strength between FW mode and SHW mode, and the involved nonlinear coefficient components of ${\ensuremath{\chi}}^{(2)}$. Finally, we have analytically derived the explicit formula that allows for direct calculation of the SHG efficiency as a function of the interaction length of FW mode and SHW mode, the nonlinear coupling coefficient, and the FW pump intensity, for both the small signal and general large signal situations. Our analytical theory and formulation can greatly facilitate the deep understanding of nonlinear optical interaction physics and provide a convenient tool for accurate quantitative evaluation of the SHG energy conversion efficiency of a pump laser in nanoscale LN single-crystal thin films. This analytical theory can also benefit for the design of nanoscale nonlinear optical devices based on the material platform of LN and other nonlinear crystal thin films.

Four wave mixing and compensating losses in metamaterials

The conditions under which losses can be compensated in the case of propagation of an backward signal wave under parametric four-wave interaction are analyzed. It is shown that, in the presence of a parametric coupling between forward and backward waves, compensation of signal wave losses by losses of direct waves will allow the parametric amplification and generation of the backward wave to be realized at the threshold pump amplitude. An analytical expression is obtained for the threshold pumping amplitude under phase-matching conditions. It is shown that the threshold pump amplitude increases with increasing losses, the input intensity of the idler wave, and with increasing nonlinear coupling coefficients for pump waves. As a consequence, it is possible to control the threshold pump intensity. and it is possible to obtain significant amplification in the metamaterial, as well as parametric generation of the backward wave.

Mitigate transverse mode instability by linear inner-cladding fiber

Transverse mode instability (TMI) limits power scaling of fiber lasers. A semianalytical model is established to calculate the TMI threshold in high-power fiber laser systems of the multi-kW-class. A linear inner-cladding fiber can mitigate the TMI effect by smoothing the heat profile and decreasing the nonlinear coupling coefficient along the fiber. We investigate strong pump absorption of a linear inner-cladding fiber, which leads to shorter fiber length. Utilizing a 915-nm copumping scheme, the linear inner-cladding fiber can realize 10-kW output power in single-mode regime theoretically.

Investigation of LP- and Vector-Modes for the Analysis of Space-Division Multiplexed Systems in the Nonlinear Regime

Space-division multiplexing in multimode fibers is a very promising approach to overcome the shortcoming of capacity in long-haul optical transmission systems. In this paper, we present an analysis of different mode representations in multimode fibers. We resume the properties and the interrelations of linearly polarized and vectorial modes. We take a look at the coupled nonlinear Schrodinger equation and Manakov equations for strongly coupled mode groups. The nonlinear coupling coefficient of the Manakov equation is investigated for both mode bases, in order to verify if the approximated linearly polarized modes are a valid representation for the analysis of nonlinearities in space-division multiplexed systems. Even though the effective mode areas differ considerably between LP- and vector modes, the simulated coupling coefficient shows a good agreement between both models. The results indicate that the mode basis does not affect the nonlinear parameter. For the analysis the field distributions of the modes are numerically calculated with a vector finite difference modesolver. Finally the simulated results are verified analytically.

Three-wave scattering in magnetized plasmas: From cold fluid to quantized Lagrangian.

Large amplitude waves in magnetized plasmas, generated either by external pumps or internal instabilities, can scatter via three-wave interactions. While three-wave scattering is well known in collimated geometry, what happens when waves propagate at angles with one another in magnetized plasmas remains largely unknown, mainly due to the analytical difficulty of this problem. In this paper, we overcome this analytical difficulty and find a convenient formula for three-wave coupling coefficient in cold, uniform, magnetized, and collisionless plasmas in the most general geometry. This is achieved by systematically solving the fluid-Maxwell model to second order using a multiscale perturbative expansion. The general formula for the coupling coefficient becomes transparent when we reformulate it as the scattering matrix element of a quantized Lagrangian. Using the quantized Lagrangian, it is possible to bypass the perturbative solution and directly obtain the nonlinear coupling coefficient from the linear response of the plasma. To illustrate how to evaluate the cold coupling coefficient, we give a set of examples where the participating waves are either quasitransverse or quasilongitudinal. In these examples, we determine the angular dependence of three-wave scattering, and demonstrate that backscattering is not necessarily the strongest scattering channel in magnetized plasmas, in contrast to what happens in unmagnetized plasmas. Our approach gives a more complete picture, beyond the simple collimated geometry, of how injected waves can decay in magnetic confinement devices, as well as how lasers can be scattered in magnetized plasma targets.

Correlation of quadrature amplitude fluctuations during the intracavity generation of second harmonic

For the process of intracavity generation of the second harmonic, the dynamics of correlation of quadrature amplitudes fluctuations of the fundamental and the second harmonic modes is studied depending on the nonlinear coupling coefficient between the modes. It was shown that in this system the entangled states of field related to variables of quadrature amplitudes may be obtained depending on the nonlinear coupling coefficient. It was also shown that the entanglement of the states of field modes related to one quadrature amplitude may vanish depending on the value of nonlinear coupling coefficient, whereas the states of field modes related to the other quadrature amplitude stay entangled.

Influence of a nonlinear coupling on the supratransmission effect in modified sine-Gordon and Klein–Gordon lattices

In this paper, we analyze the conditions leading to the nonlinear supratransmission phenomenon in two different models: a modified fifth order Klein–Gordon system and a modified sine-Gordon system. The modified models considered here are those with mixed coupling, the pure linear coupling being associated with a nonlinear coupling. Especially, we numerically quantify the influence of the nonlinear coupling coefficient on the threshold amplitude which triggers the nonlinear supratransmission phenomenon. Our main result shows that, in both models, when the nonlinear coupling coefficient increases, the threshold amplitude triggering the nonlinear supratransmission phenomenon decreases.

Quantum dynamics of intracavity third-subharmonic generation

The quantum dynamics of the mean number of photons and quantum entropy of interacting modes, as well as the Wigner function of the stationary state of the fundamental mode and the third subharmonic mode has been investigated for the intracavity third-subharmonic generation. It is shown that the quantum dynamics of the system depends strongly on the nonlinear coupling coefficient between the modes. It is also demonstrated that, in the steady-state limit, depending on the intermodal coupling coefficient, the fundamental mode can be either in a pure coherent state, or in a squeezed state, or in a pure vacuum state. The third subharmonic mode in the subthreshold regime of generation of this mode is in the vacuum state. The Wigner function is squeezed over three sides of an equilateral triangle (squeezed vacuum). The quantum entropy of this state is nonzero. It is also shown that the third subharmonic mode, depending on the nonlinear coupling coefficient in the steady-state limit, can be localized in the three-component state with the same probability of detecting a field in each coherent component of the state and with the presence of quantummechanical interference between the state components. The mean number of photons in this state is smaller than unity. Depending on the nonlinear coupling coefficient, the third subharmonic mode can also be localized in the three-component state, which is a statistical mixture of three squeezed states.